COSMO-SAC study of electrolytes for battery application

1 FACULTAD DE CIENCIAS TRABAJO FIN DE GRADO Grado en química COSMO-SAC study of electrolytes for battery application Autor/a: Álvaro De La Fuente Villanueva Tutor/es/as: María Carmen Barrientos Benito, Sondre Kvalvåg Schnell Año: 2023 2 Preface This project is made as a specialization course in materials technology TMT4500 at the Norwegian university of science and technology (NTNU), and later presented as a bachelor’s thesis at Universidad de Valladolid (Uva). I would like to acknowledge my supervisor Sondre for helping me with the problems and the project as well as my family and friends for the emotional support. Abstract In this project, we use a semi-empirical quantum chemistry method named COSMO-SAC for evaluating the activity coefficients and the Gibbs free energy of mixing of the most common organic solvent binary mixtures used in Lithium-ion batteries. These are made of four carbonic acid derivates: dimethyl carbonate (DMC), diethyl carbonate (DEC), ethylene carbonate (EC) and propylene carbonate (PC). A DFT study prior to the use of COSMO-SAC was performed, emphasizing on vibrational analysis and electrostatic potential surface mapping. Activity coefficients are studied at different conditions of temperature, composition, and mole fraction. Both excess free energy and free energy of mixing are also studied. The results fulfil the expected behaviours, but they are not precise. For some specific conditions of temperature and concentration, the model is not suitable. Resumen En este trabajo, se ha utilizado un método semi-empírico mecanocuántico denominado COSMO-SAC para evaluar los coeficientes de actividad y energías libres de mezcla para las mezclas binarias más comunes en baterías de ión-litio. Éstas están constituidas por derivados del ácido carbónico: carbonato de dimetilo (DMC), carbonato de dietilo (DEC), carbonato de etileno (EC) y carbonato de propileno (PC). Se realizó un estudio DFT previo al uso de COSMO-SAC, enfatizado en análisis vibracional y mapeado de superficies de potencial electrostático. Los coeficientes de actividad fueron estudiados a diferentes condiciones de temperatura, composición y fracción molar. Ambas energías libres (exceso y mezcla) fueron estudiadas también. Los resultados son afines con lo esperado, pero no son precisos. Para algunas condiciones de temperatura y concentración, el modelo no es aplicable. 3 Index 1. Introduction .................................................................................................................................. 5 1.1. Background and motivation........................................................................................................................ 5 1.1.1 Batteries .............................................................................................................................................................. 5 1.1.2 Predictive models ................................................................................................................................................ 6 2. Objectives ..................................................................................................................................... 7 3. Theory ........................................................................................................................................... 9 3.1. Density functional theory (DFT) .................................................................................................................. 9 3.1.1. Method description ........................................................................................................................................... 10 3.1.2. DFT functionals .................................................................................................................................................. 11 3.1.3. Basis sets ........................................................................................................................................................... 12 3.1.4. Optimization and vibrational analysis ................................................................................................................ 13 3.2. Sigma profile plotting ............................................................................................................................... 14 3.3. Splitting the sigma profile contributions .................................................................................................. 16 3.4. COSMO-SAC 2002 for activity coefficients ................................................................................................ 16 3.5. COSMO-SAC 2010 for activity coefficients ................................................................................................ 19 3.6. Dispersive interactions ............................................................................................................................. 20 4. Method ....................................................................................................................................... 22 4.1. Databases ................................................................................................................................................. 22 4.2. Implementation of the code ..................................................................................................................... 22 4.3. Activity coefficients................................................................................................................................... 23 4.4. Excess Gibbs free energy .......................................................................................................................... 23 5. Results and discussions ............................................................................................................... 25 5.1. DFT results ................................................................................................................................................ 25 5.1.1. Energy calculation ............................................................................................................................................. 25 5.1.2. Optimized geometry .......................................................................................................................................... 26 5.1.3. Infrared spectra ................................................................................................................................................. 26 5.1.4. Electrostatic potential ....................................................................................................................................... 27 5.2. Activity coefficients................................................................................................................................... 27 5.2.1. Composition ...................................................................................................................................................... 27 5.2.2. Temperature dependence ................................................................................................................................. 28 5.2.3. Components dependence ................................................................................................................................. 29 5.3. Gibbs free energy of mixing ...................................................................................................................... 30 6. Conclusion ................................................................................................................................... 32 7. Further work ............................................................................................................................... 33 8. References................................................................................................................................... 34 9. Appendices .................................................................................................................................. 37 Appendix A: Activity coefficient profiles .............................................................................................. 37 Appendix B-Excess free energy of mixing ............................................................................................. 41 Appendix C: Gibbs free energy of mixing ............................................................................................. 44 Appendix D: Infrared vibrational spectra ............................................................................................. 48 Appendix E: Electrostatic potential surfaces ........................................................................................ 50 4 List of figures and tables Table 1. Structure and relevant properties (dielectric constant ε and viscosity η) of carbonic acid esters for battery applications. Table 2. Parameters for COSMO-SAC 2002 Table 3. Parameters for COSMO-SAC 2010 and their values. Table 4. Values of εi /Kb for different atoms and hybridizations in COSMO-SAC-dsp Table 5. Identifiers for carbonate esters. Table 6: Energies calculated using DFT theory with different functionals and basis for the minimum energy conformer. Table 7: Ratio of excess free energy in equimolar mixtures. Figure 1. Sigma profile 𝑝𝜎 for DMC (616-49-1) and DEC (96-49-1) in both databases Figure 2. Temperature dependence of ln(γ) for three mixtures of DMC and DEC. Figure 3. Activity coefficients map for different mixtures containing EC at 303K 5 1. Introduction 1.1. Background and motivation 1.1.1 Batteries In these coming years, the need for new batteries is in rise. The energetic demand is increasing way faster than the research in new and more sustainable ways of producing and storing it. For this reason, there is some research in batteries now focusing on developing new ones based on, for example, Al-ion instead. Aluminium is one of the most common elements in earth crust, and its obtaining method is widely studied and improved each year. Potassium batteries are also growing interest since it is chemically similar to Li, has a lower reduction potential, and is more abundant and easier to refine. However, the dominance of Li-ion batteries (LIB) will go on for several years from now i . Li-ion batteries are, undoubtedly, the most used batteries throughout the world mainly because of their high charge density. LIB are capable of storing enormous amounts of energy in a compact and light device. Some other advantages are the low self-discharge rate, which would mean an efficiency loss, and the good cycle life, which means that they work properly after many cycles of charge-discharge. Their usage is being studied not only for improving electronic devices such as laptops, mobile phones etc., but also, for electric vehicles. Research in LIB is nowadays focused in perfectioning the three parts of the battery [23]: ➢ The anode, by changing its composition from graphene to Li alloys with tin or silicon that present a higher capacity. ➢ The cathode, by using other Li oxides such as the lithium-nickel-manganese oxide (LNMO). ➢ The electrolyte, by using polymers, gel, or solid-state electrolytes as well as ionic liquids. One of the biggest problems of LIB is the recycling process [30]. The most used electrolytes are made of a Li salt such as LiPF6 (lithium hexafluorophosphate), LiTFSI (Lithium bis(trifluoromethane sulfonyl) imide), etc., dissolved in an organic solvent with additives. This organic solvent is a mixture of carbonic acid esters. These chemicals are toxic, volatile and may decompose by thermal decomposition or reacting with air and water, consequently generating formaldehyde, acetaldehyde, ethanol, methanol, or formic acid [28]. 6 All the points covered above are time consuming, so the usage of predictive models might be a solution to this problem. 1.1.2 Predictive models Predictive models are growing massive interest by not only research groups, but also the chemical industry for several reasons. Some of them being not needing to buy the compounds for studying their properties, the lack of risk involved in these measurements, time saving, free software for academic purposes in general and accuracy in the obtained data. COSMO-SAC (Conductor-like Screening Model for segment activity coefficients) is, without doubt, a useful and promising tool. Activity coefficients are truly versatile for refining thermodynamic properties of real mixtures. Many other properties can be obtained e.g., vapour-liquid equilibrium, solubility [10] [24], partition coefficients, viscosity, enthalpy of mixture [16] [21] etc. 7 2. Objectives The main problem resides in the need of an electrolytic mixture that presents some qualities: being a one-phase liquid at room temperature, being able to dissolve the ion, enabling its transport between the electrodes, thermal stability etc. This search would take years of trying and repeating mixtures with different components, so we decided to use a computer software called COSMO-SAC[4]. This tool predicts different thermodynamical properties such as activity coefficients, liquid-vapor phase equilibrium etc. by studying the charge density of fragments of the molecules using quantum chemical methods. Both variants: COSMO-SAC (conductor-like screening model-segment activity coefficient, created by Lin and Sandler [4]) and COSMO-RS (conductor-like screening model for real solvents, created by Klam et al.[1]) have been used throughout the last years for different purposes such as drug development, industrial modelling for new materials etc., but we will now use an adapted version for electrolytes called eCOSMOSAC [12] (electrolyte conductor-like screening model-segment activity coefficient). The focus of this work is to study some properties of the most used electrolytic solvents present in lithium batteries. These are carbonic acid esters [25]. In general, they present a high permittivity and there are two types: cyclic and linear. The first ones dissolve Li salts such as LiTFSI and LiPF6, and the second ones add fluidity to the solution (the cyclic esters have a really high viscosity which is an inconvenience because it implies a loss of efficiency). A good mixture of solvents should be able to provide an efficient transport of Li ions between the cathode and anode [11] [13]. The components to be studied are ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC) and diethyl carbonate (DEC). (See table 1 below) 8 Table 1. Structure and relevant properties (dielectric constant ε and viscosity η) of carbonic acid esters for battery applications. DMC DEC EC PC Structure Cyclicity Linear Linear Cyclic Cyclic Tm (K)** 278.2 198.2 311.2 220.3 Tb (K)** 363.5 400 516.7 513.2 ε 3.107 2.805 89.78 64.92 η (mPa-s) 0.59 0.75 1.93 2.52 *These values were obtained experimentally by Lide [31] **These values were obtained in the NIST online database [14] By doing this, the applicability of COSMO-SAC in battery research will be studied as well as give some data on these electrolytic mixtures for a future enhancement or development of a solvent for a new battery. In addition, in this study, we have performed a theoretical study within the Density Functional Theory (DFT) context for the ground-level energy of the four molecules (ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC) and diethyl carbonate (DEC)), as well as a vibrational frequency study. 9 3. Theory To carry out this study we are using COSMO-SAC. Both COSMO models, COSMO-RS (real solvent) and COSMO-SAC are based on UNIFAC [19] [16] (semi-empirical method for activity coefficients calculation): instead of using interactions between the different functional groups of a molecule to describe the properties of a real mixture, it rather considers interactions between several segments of constant charge density. Using the different data given by these segments, we are able to calculate the activity coefficients of a specific mixture of components. It is also possible to study the properties of ionic liquids [17] [26] and electrolytes combining it with the Pitzer-Debye-Hückel model [12]. This requires a density functional theory (DFT) calculation to obtain these segments and their respective charge density. Specifically, Dmol3, Gaussian and GAMESS software are used for this purpose. The DFT calculations must perform the following steps: • Set a fixed location for all the nuclei. • Divide the molecule in segments of different electronic density. • Calculate the surface area and volume of the molecule and the different segments. • Define the position of the segments as well as their charge density. In COSMO-SAC-2010, the program also considers which segment is related to a hydrogen-bonding atom, thus classifying them into three groups (see 3.5): ➢ Not hydrogen-bonding atom (NHB). ➢ OH: the atom correlated to the segment is either an O or H atom. ➢ OT: the atom is N, F, H (bonded to F or N) or O not bonded to H. 3.1. Density functional theory (DFT) Density functional theory is one of the most used computational procedures applied to chemistry. The method is based on the assumption that the electronic energy of a molecule can be described using a function that accounts for the electron probability density (ρ) and depends on the point of space that is being studied (r). Therefore, the energy is treated as a functional of this electron density function. This is written as E[ρ(r)]. DFT is not only useful because it accounts for the correlation energy, but also because the use of only one function is necessary for a N-electron molecule without adding constraints. 16 3.3. Splitting the sigma profile contributions At this point is where the intermolecular interactions such as hydrogen-bonding should be taken into account according to Lin et al. [3] If this is the case, the corresponding sigma profile can be expressed as an addition of two terms: 𝑝(𝜎)=𝑝(𝜎)𝑁𝐻𝐵+𝑝(𝜎)𝐻𝐵 (19) Being each of them defined as gaussian functions according to Wang et al. [3]: 𝑝(𝜎)𝐻𝐵=1−𝑒𝑥𝑝(−𝜎2 2𝜎02) (20) Eq. (20) describes the sigma profile of all hydrogen bonding atoms (N, O, F and H) where σ0 = 0.007 e/Å2. Therefore, the different sigma profiles are expressed as it follows: 𝑝(𝜎)𝑁𝐻𝐵=𝐴𝑖𝑁𝐻𝐵(𝜎) 𝐴𝑖+𝐴𝑖𝐻𝐵(𝜎) 𝐴𝑖[1−𝑝(𝜎)𝐻𝐵] (21) 𝑝(𝜎)𝑂𝐻=𝐴𝑖𝑂𝐻(𝜎) 𝐴𝑖𝑝(𝜎)𝐻𝐵 (22) 𝑝(𝜎)𝑂𝑇=𝐴𝑖𝑂𝑇(𝜎) 𝐴𝑖𝑝(𝜎)𝐻𝐵 (23) Where 𝐴𝑖𝐻𝐵=𝐴𝑖𝑂𝐻+𝐴𝑖𝑂𝑇 is the surface area of all hydrogen-bonding segments and being 𝐴𝑖𝑂𝐻 and 𝐴𝑖𝑂𝑇 the surface areas of hydroxyl groups and the rest of the hydrogenbonding atoms respectively. Sigma profiles can usually be found in several databases. In this case we are using two of them: Virginia Tech University and Delaware University and can be reached from different sources [8] [9] [10]. In these databases, a wide variety of sigma profiles for different compounds has been validated and compared to experimental data to be used. 3.4. COSMO-SAC 2002 for activity coefficients Once obtained the sigma profile, the next step is to calculate the natural logarithm of the activity coefficients. 17 For a mixture of component i in a solvent S, the activity coefficient is described by Lin and Sandler [4] as: ln(𝛾𝑖,𝑆)=ln(𝛾𝑖,𝑆 𝑐)+ln(𝛾𝑖,𝑆 𝑟) (24) The first term on the right side is called natural logarithm of the combinatorial activity coefficient and describes the activity coefficient according to the molecular structures of the components in the mixture as follows: ln(𝛾𝑖,𝑆 𝑐)=ln(𝜙𝑖 𝑥𝑖)+𝑧2𝑞𝑖ln(𝜃𝑖 𝜙𝑖)+𝑙𝑖−𝜙𝑖 𝑥𝑖∑𝑥𝑗𝑙𝑗 (25) 𝑗 As one can tell, equation (25) is a Staverman-Guggenheim combinatorial term, where the different parameters are calculated as: 𝜃𝑖=𝑥𝑖𝑞𝑖 ∑𝑥𝑗𝑞𝑗𝑗 (26) 𝜙𝑖=𝑥𝑖𝑟𝑖 ∑𝑥𝑗𝑟𝑗𝑗 (27) 𝑙𝑖=𝑧2(𝑟𝑖−𝑞𝑖)−(𝑟𝑖−1) (28) 𝑧 is the coordination number, 𝑥𝑖 and 𝑥𝑗 are the mole fraction of components i and j in the mixture, and: 𝑟𝑖=𝑉𝑖 𝑟0 (29) 𝑞𝑖=𝐴𝑖 𝑞0 (30) Where 𝑟0=66.69 Å3 and 𝑞0=79.53 Å2 are the normalized values for volume and surface area. For infinite dilution, the mole fraction of one component is almost equal to 0, making equations (26) and (27) not viable. This results in rewriting them as: 𝜃𝑖 𝑥𝑖=𝑞𝑖 ∑𝑥𝑗𝑞𝑗𝑗 (31) 𝜙𝑖 𝑥𝑖=𝑟𝑖 ∑𝑥𝑗𝑟𝑗𝑗 (32) 𝜃𝑖 𝜙𝑖=𝜃𝑖𝑥𝑖 ⁄ 𝜙𝑖𝑥𝑖 ⁄ (33) The second term in eq. (24) gives a correction due to the residual activity coefficient generated by the interaction between charge densities of the molecules. According to the authors, this should be calculated as: 18 ln(𝛾𝑖,𝑆 𝑟)=𝑛𝑖∑𝑝𝑖(𝜎𝑚)[ln(𝛤𝑠(𝜎𝑚))−ln(𝛤𝑖(𝜎𝑚))] 𝜎𝑚 (34) Where 𝑛𝑖 is the number of surface segments with a segment surface area aeff and can be described as: 𝑛𝑖=𝐴𝑖 𝑎𝑒𝑓𝑓 (35) 𝜎𝑚 is the screening charge density, 𝑝𝑖(𝜎𝑚) is the probability of a segment with a specific screening charge density 𝜎𝑚, which can be calculated as: 𝑝𝑖(𝜎𝑚)=𝐴𝑖(𝜎𝑚) 𝐴𝑖 (36) and 𝛤𝑠(𝜎𝑚),𝛤𝑖(𝜎𝑚) are the activity coefficients of segment m in the mixture and in the pure component respectively. These last terms are derived as: ln (𝛤𝑠(𝜎𝑚))=−𝑙𝑛{∑𝑝𝑠(𝜎𝑛)𝛤𝑠(𝜎𝑛)𝑒𝑥𝑝[−∆𝑊(𝜎𝑚,𝜎𝑛) 𝑅𝑇 ] 𝜎𝑛} (37) ln(𝛤𝑖(𝜎𝑚))=−𝑙𝑛{∑𝑝𝑖(𝜎𝑛)𝛤𝑖(𝜎𝑛)𝑒𝑥𝑝[−∆𝑊(𝜎𝑚,𝜎𝑛) 𝑅𝑇 ] 𝜎𝑛} (38) Here, a new term ∆𝑊(𝜎𝑚,𝜎𝑛) is introduced. This is known as the exchange energy and to calculate it, we use the following expression: ∆𝑊(𝜎𝑚,𝜎𝑛)=(𝛼′ 2)(𝜎𝑚+𝜎𝑛)2+𝑐ℎ𝑏𝑚𝑎𝑥[0,𝜎𝑎𝑐𝑐−𝜎ℎ𝑏]𝑚𝑖𝑛[0,𝜎𝑑𝑜𝑛+𝜎ℎ𝑏] (39) The term 𝛼′ is the misfit energy of electrostatic interactions, 𝑐ℎ𝑏 is a constant and 𝜎ℎ𝑏 is the cut-off energy of the hydrogen bonding. 𝜎𝑎𝑐𝑐 and 𝜎𝑑𝑜𝑛 were described as the maximum and minimum values of 𝜎𝑚 and 𝜎𝑛. Table 2. Parameters for COSMO-SAC 2002 Parameter Value 𝛼′ 16466.72 Kcal Å4mol-1e-2 𝑐ℎ𝑏 85580 Kcal Å4mol-1e-2 𝜎ℎ𝑏 0.0084 eÅ−2 19 3.5. COSMO-SAC 2010 for activity coefficients Hsieh et al. [6] proposed modifications in 2010 to make the results for activity coefficients more precise. According to them, the exchange energy should be rewritten as: ∆𝑊(𝜎𝑚 𝑡,𝜎𝑛𝑠)=𝑐𝐸𝑆(𝑇)(𝜎𝑚 𝑡+ 𝜎𝑛𝑠)2−𝑐ℎ𝑏(𝜎𝑚 𝑡,𝜎𝑛𝑠)(𝜎𝑚 𝑡−𝜎𝑛𝑠)2 (40) 𝜎𝑚 𝑡 and 𝜎𝑛𝑠 are two different types of sigma profiles, regarding the hydrogen bonding interactions, and the correction term 𝑐𝐸𝑆 accounts the electrostatic interactions and is dependent on temperature: 𝑐𝐸𝑆=𝐴𝐸𝑆+𝐵𝐸𝑆 𝑇2 (41) The second modification is the division of the hydrogen bonding into the three types mentioned before. The value of 𝑐ℎ𝑏 changes depending on the type of hydrogen bonding: 𝑐ℎ𝑏(𝜎𝑚 𝑡,𝜎𝑛𝑠)={ 𝑐𝑂𝐻−𝑂𝐻 𝑖𝑓 𝑠=𝑡=𝑂𝐻 𝑎𝑛𝑑 𝜎𝑚 𝑡 𝜎𝑛𝑠<0 𝑐𝑂𝐻−𝑂𝑇 𝑖𝑓 𝑠=𝑂𝐻,𝑡=𝑂𝑇 𝑎𝑛𝑑 𝜎𝑚 𝑡 𝜎𝑛𝑠<0 𝑐𝑂𝑇−𝑂𝑇 𝑖𝑓 𝑠=𝑡=𝑂𝑇 𝑎𝑛𝑑 𝜎𝑚 𝑡 𝜎𝑛𝑠<0 (42) And 0 otherwise. Due to this separation, a new term must be added to equation (34): ln(𝛾𝑖,𝑆 𝑟)=𝑛𝑖∑ ∑𝑝𝑖𝑡(𝜎𝑚𝑡)[ln(𝛤𝑠𝑡(𝜎𝑚𝑡))−ln(𝛤𝑖𝑡(𝜎𝑚𝑡))] 𝜎𝑚 𝑛ℎ𝑏,𝑂𝐻,𝑂𝑇 𝑡 (43) And thus, equation (37) becomes: ln (𝛤𝑠𝑡(𝜎𝑚𝑡))=−𝑙𝑛{ ∑ ∑𝑝𝑠𝑠(𝜎𝑛𝑠)𝛤𝑠𝑠(𝜎𝑛𝑠)𝑒𝑥𝑝[−∆𝑊(𝜎𝑚𝑡,𝜎𝑛𝑠) 𝑅𝑇 ] 𝜎𝑛 𝑛ℎ𝑏,𝑂𝐻,𝑂𝑇 𝑠} (44) The same change is also used in equation (38). ln (𝛤𝑖𝑡(𝜎𝑚𝑡))=−𝑙𝑛{ ∑ ∑𝑝𝑖𝑠(𝜎𝑛𝑠)𝛤𝑖𝑠(𝜎𝑛𝑠)𝑒𝑥𝑝[−∆𝑊(𝜎𝑚𝑡,𝜎𝑛𝑠) 𝑅𝑇 ] 𝜎𝑛 𝑛ℎ𝑏,𝑂𝐻,𝑂𝑇 𝑖} (45) All the parameters for COSMO-SAC 2010 are implemented in the code as shown in Table 3: 20 Table 3. Parameters for COSMO-SAC 2010 and their values. Parameter Value q0 79.53 Å2 r0 66.69 Å3 z 10 aeff 7.25 Å2 reff (aeff/π)0.5 fdecay 3.57 cOH-OH 4013.78 kcal Å4 mol-1 e-2 cOT-OT 932.31 kcal Å4 mol-1 e-2 cOH-OT 3016.43 kcal Å4 mol-1 e-2 σ0 0.007 e Å-2 AES 6525.69 kcal Å4 mol-1 e-2 BES 1.4859 E8 kcal Å4 K2 mol-1 e-2 NA 6.022140758 E23 mol-1 kB 1.38064903 E-23 J K-1 R 4184 kcal mol-1 K-1 3.6. Dispersive interactions Hsieh et al. also considered the interaction between molecules due to dispersive interactions [6]. This way, a new term was added to equation (24): ln(𝛾𝑖,𝑆)=ln(𝛾𝑖,𝑆 𝑐)+ln(𝛾𝑖,𝑆 𝑟)+ ln(𝛾𝑖,𝑆 𝑑𝑠𝑝) (46) The combinatorial and residual terms are calculated the same way. However, the new contribution to the activity coefficient is slightly different: ln(𝛾𝑖,𝑆 𝑑𝑠𝑝)=𝐴𝑥𝑖2 (47) Where A is a parameter calculated as follows: 𝐴=𝑤[0.5(𝜀1 𝑘𝑏+𝜀2 𝑘𝑏)−√𝜀1 𝑘𝑏𝜀2 𝑘𝑏] (48) kb is the Boltzmann’s constant and 𝜀𝑖 is the dispersion parameter which has different values for different atoms (see Table 4) and their values are obtained from experimental data. W can take different values according to the functional groups in the molecule: 21 𝑤= { −0.27027 𝐾−1 𝑖𝑓 𝑤𝑎𝑡𝑒𝑟+ℎ𝑏−𝑜𝑛𝑙𝑦 𝑎𝑐𝑐𝑒𝑝𝑡𝑜𝑟 −0.27027 𝐾−1 𝑖𝑓 𝐶𝑂𝑂𝐻+(𝑛ℎ𝑏 𝑜𝑟 ℎ𝑏−𝑑𝑜𝑛𝑜𝑟 𝑎𝑛𝑑 𝑎𝑐𝑐𝑒𝑝𝑡𝑜𝑟) −0.27027 𝐾−1 𝑖𝑓 𝑤𝑎𝑡𝑒𝑟+𝐶𝑂𝑂𝐻 0.27027 𝐾−1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (49) COOH refers to the carboxyl group, nhb are molecules that cannot make hydrogen bonds, hb-only acceptor are molecules that are only capable of accepting protons from a hb molecule and hb-donor and acceptor, as the name suggests, are molecules that can be both donor and acceptor of protons. Table 4. Values of εi /Kb for different atoms and hybridizations in COSMO-SAC-dsp Atom type (𝜀𝑖/𝑘𝑏) / K C (sp3) 115.7023 C (sp2) 117.4650 C (sp) 66.0691 N (sp3) 15.4901 N (sp2) 84.6268 N (sp) 109.6621 -O95.6184 =O −11.0549 F 52.9318 Cl 104.2534 H (water) 58.3301 H (OH) 19.3477 H (NH) 141.1709 H (other) 0 Other Invalid 22 4. Method 4.1. Databases The first step in order to use COSMO-SAC is to generate the sigma profiles. For this purpose, a density functional theory (DFT) calculation must be performed. Authors normally use Dmol3 because an additional COSMO-based module is added [29]. DFT is a molecular structure dependent method, so the choice of a relevant structure is a crucial step. So, a geometry optimization is also performed by choosing random starting points and minimizing its energy to get a global minimum. Once obtained the structure, we run the calculations specifying in the input file which parameters we are interested in, this being: surface area, volume, and charge density of the segments. Afterwards, the sigma profile is generated as we mentioned in the theory part. However, in this work we are not following this process. This is because DFT is a complex and time-consuming method and must be optimized for the specific level of calculation. Instead, we are using two databases developed by two universities: Virginia Tech University (VT) [9] [10] and University of Delaware (UD). The first one was earlier generated, so the latest upgrade in COSMO-SAC, which corresponds to the dispersive contribution, is not implemented in the code. But VT can be used to calculate activity coefficients for ternary mixtures alike UD. 4.2. Implementation of the code COSMO-SAC is an open-source program, and its code is stored in a git-hub page thanks to Bell et al. [8] https://github.com/usnistgov/COSMOSAC , where one can also find some examples on how to make a script. These files are normally written using python. We paid close attention to the easy_COSMOSAC.py example, in which you can set some parameters and get the activity coefficients for a binary or tertiary mixture. These parameters are temperature, mole fraction and identifiers for the components in the mixture (see Table 5). These identifiers can be found in the compound lists for the databases and several of them are implemented (name, CAS number, InChiKey …), however, a bad choice in the identifiers could lead to a problem, so we chose to use CAS numbers as they are unique for each chemical. 23 Table 5. Identifiers for carbonate esters. DMC DEC EC PC ID (UD) 325 841 843 487 ID (VT) 1242 704 678 1224 Name (UD) DIMETHYL_CARBONATE DIETHYL_CARBONATE ETHYLENE_CARBONATE PROPYLENE_CARBONATE Name (VT) DIMETHYL-CARBONATE DIETHYL-CARBONATE ETHYLENE-CARBONATE PROPYLENE-CARBONATE CAS# 616-38-6 105-58-8 96-49-1 108-32-7 SMILES COC(=O)OC CCOC(=O)OCC C1(=O)OCCO1 C1(=O)OC[C@@H](O1)C INCHIKEY IEJIGPNLZYLLBPUHFFFAOYSA-N OIFBSDVPJOWBCHUHFFFAOYSA-N KMTRUDSVKNLOMYUHFFFAOYSA-N RUOJZAUFBMNUDXVKHMYHEASA-N 4.3. Activity coefficients The next step is to use the sigma profiles stored in the databases for calculating the activity coefficients using both models: COSMO-SAC 2002 and COSMO-SAC 2010 (dsp). We should also look at how the activity coefficients depend on the input parameters, these being: temperature, composition, and components in the mixture. 4.4. Excess Gibbs free energy Excess properties are characteristic of non-ideal behaviours. Excess free energy is defined as the extra energy needed to mix two (or more) components. It can be related to the lost work in a mixing process, and this is not optimal for our battery design. The excess free energy is calculated as follows [7] [15] : 𝐺𝐸=𝑅𝑇∑ 𝑥𝑖 ln(γ 𝑖) ( 𝑛 𝑖=1 50) Being γ 𝑖 the activity coefficient obtained by COSMO-SAC calculations, xi the mole fraction of the component i in a mixture and R is the ideal gas constant. The expression for mixing free energy is: ∆𝐺𝑚𝑖𝑥=∆𝐺𝑖𝑑𝑒𝑎𝑙+∆𝐺𝐸=𝑅𝑇∑𝑥𝑖ln(𝑥𝑖)+𝑥𝑖ln(𝛾𝑖) 𝑛 𝑖=1 (51) 24 Note that the first term is always negative or 0 (for the pure component), the consequence of this is that the excess free energy is the property that determines whether the components will mix or de-mix according to the sign: positive ∆𝐺𝑚𝑖𝑥 means de-mixing and negative, the opposite. By looking at the phase diagrams for these mixtures [22], we are expecting that all of them will mix in liquid state at 303K. 25 5. Results and discussions 5.1. DFT results 5.1.1. Energy calculation In this study, we performed a DFT calculation for the ground-level energy of the four molecules, as well as a vibrational frequency study. For this work, three basis and two functionals were used, these being respectively: 6-31G, 6-311G, aug-cc-pVDZ and augcc-pVTZ (the basis sets), B3LYP and B2PLYPD3* (the functionals). Table 6: Energies calculated using DFT theory with different functionals and basis for the minimum energy conformer. Molecule Functional Basis set Energy (H) Ethylene carbonate (EC) B3LYP 6-31G -342.268881 6-311G -342.36408 aug-cc-pVTZ -342.53782 B2PLYPD3 aug-cc-pVTZ -342.30516 Propylene carbonate (PC) B3LYP 6-31G -381.58185 6-311G -381.68532 aug-cc-pVTZ -381.8731 B2PLYPD3 aug-cc-pVTZ -381.604 Dimethyl carbonate (DMC) B3LYP 6-31G -343.48367 6-311G -343.58093 aug-cc-pVTZ -343.75094 B2PLYPD3 aug-cc-pVDZ -343.35471 Diethyl carbonate (DEC) B3LYP 6-31G -422.10473 6-311G -422.21838 aug-cc-pVTZ -422.41755 B2PLYPD3 aug-cc-pVDZ -421.90935 The results obtained in the table above were calculated using Gaussian 16*. In the case of DMC and DEC, we used as geometry input a Z-matrix to force the C2v geometry. The reasons for doing this is that we expect this geometry (it looks like there is a rotation axis of 180º and a vertical reflexion plane, both centred in the carbonate group) and that way we solve some calculation problems due to molecular flexibility of the linear species. B2PLYP/aug-cc-pVTZ level of calculation for DEC and DMC was not possible due to memory requirements, so a lower level was used. 32 6. Conclusion In this work, we calculated activity coefficients, an important thermodynamic property that connects the ideal expressions and reality. The non-ideal behaviour is, in some processes, relevant and must be taken into account. We covered the following topics along the project: 1 Density functional theory was described and used, as a previous study on the molecules of interest. 2 An insight into COSMO-SAC and its working mechanisms was given, as well as some notes on its implementation. 3 We generated the activity coefficient plot at 303K and different concentrations for each binary mixture containing carbonic acid esters. Here, we also realized that both databases give back different values for most of the mixtures. 4 We had a look at the temperature dependence of the activity coefficients in the DMC+DEC mixture and assumed the same changes with temperature in different mixtures. We could see that phase transitions are not considered by COSMO-SAC. 5 The activity coefficient map for two components gave us some information about the interactions between them. In this case, the fixed component was EC due to its high performance in Li batteries. We also saw that changing the mole fraction of EC, has an effect on the differences between components. 6 Lastly, we calculated one of the most important properties for an electrolytic solvent: mixing free energy. The results met the experimental calculations as these four components were supposed to mix at 30ºC. We came to the conclusion that the non-ideal interactions between carbonic acid esters are, in general, not high enough to make the mixing free energy positive, which means that the components will not de-mix. In general, we generated some data related to carbonic acid esters in electrolytic solvents, by taking the data from two databases. Apart from that, we validated the data in these databases as well as the proper functionality and adaptability of COSMO-SAC in battery research. 33 7. Further work The next step after this project would be performing a DFT calculation of some Li electrolytes (LiPF6 or LiTFSI) and proceed with the calculation of solubility in the mixtures studied in this project, enthalpies of mixing and other properties that can be derived from activity coefficients. From this starting point, new combinations of solvents can be tested in order to find better mixtures for LIB or even get a suitable mixture for a new electrolyte without measuring experimentally. Also, in future modifications of the program, someone may probably come up with a solution for the phase changing problem, specifically with gas phase, and thus make COSMO-SAC a fluid phase model instead of just a liquid model. 34 8. References [1] Klamt, A.; Jonas, V.; Burger, T.; Lohrenz, J. Refinement and Parametrization of COSMO-RS. J. Phys. Chem 1998. A, 102, 5074. [2] Lin, S-T.; Shu Wang, J. C.; Goddard, W. A. and Sandler, S.I. 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Activity coefficients for PC+EC 39 A4. Activity coefficients for PC+DEC A5. Activity coefficients for PC+DMC 40 A6. Activity coefficients for DMC+DEC 41 Appendix B-Excess free energy of mixing B1. Excess free energy for DMC+DEC B2. Excess free energy for EC+DMC 48 Appendix D: Infrared vibrational spectra D1. IR spectra of EC D2. IR spectra of PC 49 D3. IR spectra of DMC D4. IR spectra of DEC 50 Appendix E: Electrostatic potential surfaces E1. Electrostatic potential of EC 51 E2. Electrostatic potential of PC E3. Electrostatic potential of DMC 52 E4. Electrostatic potential of DEC